Question

Suppose f(x) = aln(bx) where f(e) = 12 and f'(2) = 2. Find the constants a and b.

Answer 1

`a=4`

`b=e^2`

Explanation:

We are given that

`f(x)=aln(bx)`

f(e)=12

f'(2)=2

We have to find the constants a and b

Substitute x=e

`f(e)=aln(be)`

`12=aln(be)`

`ln(be)=(12)/(a)`

`f'(x)=(a)/(x)`

Using the formula

d(lnx)/dx=1/x

`f'(2)=(a)/(2)`

`2=(a)/(2)`

`a=4`

Substitute a=4

`ln(be)=12/4=3`

`be=e^(3)`

`b=e^(3)/e`

`b=e^2`